diff --git a/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp b/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
--- a/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
@@ -3279,6 +3279,23 @@
             NotLHS, NotRHS);
       }
     }
+
+    // Pull 'not' into operands of select if both operands are one-use compares.
+    // Inverting the predicates eliminates the 'not' operation.
+    // Example:
+    //     not (select ?, (cmp TPred, ?, ?), (cmp FPred, ?, ?) -->
+    //     select ?, (cmp InvTPred, ?, ?), (cmp InvFPred, ?, ?)
+    // TODO: Canonicalize by hoisting 'not' into an arm of the select if only
+    //       1 select operand is a cmp?
+    if (auto *Sel = dyn_cast<SelectInst>(Op0)) {
+      auto *CmpT = dyn_cast<CmpInst>(Sel->getTrueValue());
+      auto *CmpF = dyn_cast<CmpInst>(Sel->getFalseValue());
+      if (CmpT && CmpF && CmpT->hasOneUse() && CmpF->hasOneUse()) {
+        CmpT->setPredicate(CmpT->getInversePredicate());
+        CmpF->setPredicate(CmpF->getInversePredicate());
+        return replaceInstUsesWith(I, Sel);
+      }
+    }
   }
 
   if (Instruction *NewXor = sinkNotIntoXor(I, Builder))
diff --git a/llvm/test/Transforms/InstCombine/not.ll b/llvm/test/Transforms/InstCombine/not.ll
--- a/llvm/test/Transforms/InstCombine/not.ll
+++ b/llvm/test/Transforms/InstCombine/not.ll
@@ -253,11 +253,10 @@
 
 define i1 @not_select_cmp_cmp(i32 %x, i32 %y, float %z, float %w, i1 %cond) {
 ; CHECK-LABEL: @not_select_cmp_cmp(
-; CHECK-NEXT:    [[CMPT:%.*]] = icmp sle i32 [[X:%.*]], [[Y:%.*]]
-; CHECK-NEXT:    [[CMPF:%.*]] = fcmp ugt float [[Z:%.*]], [[W:%.*]]
+; CHECK-NEXT:    [[CMPT:%.*]] = icmp sgt i32 [[X:%.*]], [[Y:%.*]]
+; CHECK-NEXT:    [[CMPF:%.*]] = fcmp ole float [[Z:%.*]], [[W:%.*]]
 ; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[COND:%.*]], i1 [[CMPT]], i1 [[CMPF]]
-; CHECK-NEXT:    [[NOT:%.*]] = xor i1 [[SEL]], true
-; CHECK-NEXT:    ret i1 [[NOT]]
+; CHECK-NEXT:    ret i1 [[SEL]]
 ;
   %cmpt = icmp sle i32 %x, %y
   %cmpf = fcmp ugt float %z, %w
@@ -268,6 +267,8 @@
 
 declare void @use1(i1)
 
+; TODO: Missed canonicalization - hoist 'not'?
+
 define i1 @not_select_cmp_cmp_extra_use1(i32 %x, i32 %y, float %z, float %w, i1 %cond) {
 ; CHECK-LABEL: @not_select_cmp_cmp_extra_use1(
 ; CHECK-NEXT:    [[CMPT:%.*]] = icmp sle i32 [[X:%.*]], [[Y:%.*]]
@@ -285,6 +286,8 @@
   ret i1 %not
 }
 
+; TODO: Missed canonicalization - hoist 'not'?
+
 define i1 @not_select_cmp_cmp_extra_use2(i32 %x, i32 %y, float %z, float %w, i1 %cond) {
 ; CHECK-LABEL: @not_select_cmp_cmp_extra_use2(
 ; CHECK-NEXT:    [[CMPT:%.*]] = icmp sle i32 [[X:%.*]], [[Y:%.*]]
@@ -302,6 +305,8 @@
   ret i1 %not
 }
 
+; Negative test - extra uses would require more instructions.
+
 define i1 @not_select_cmp_cmp_extra_use3(i32 %x, i32 %y, float %z, float %w, i1 %cond) {
 ; CHECK-LABEL: @not_select_cmp_cmp_extra_use3(
 ; CHECK-NEXT:    [[CMPT:%.*]] = icmp sle i32 [[X:%.*]], [[Y:%.*]]
@@ -321,6 +326,8 @@
   ret i1 %not
 }
 
+; Negative test - extra uses would require more instructions.
+
 define i1 @not_select_cmp_cmp_extra_use4(i32 %x, i32 %y, float %z, float %w, i1 %cond) {
 ; CHECK-LABEL: @not_select_cmp_cmp_extra_use4(
 ; CHECK-NEXT:    [[CMPT:%.*]] = icmp sle i32 [[X:%.*]], [[Y:%.*]]
@@ -338,6 +345,8 @@
   ret i1 %not
 }
 
+; TODO: Missed canonicalization - hoist 'not'?
+
 define i1 @not_select_cmpt(double %x, double %y, i1 %z, i1 %cond) {
 ; CHECK-LABEL: @not_select_cmpt(
 ; CHECK-NEXT:    [[CMPT:%.*]] = fcmp oeq double [[X:%.*]], [[Y:%.*]]
@@ -351,6 +360,8 @@
   ret i1 %not
 }
 
+; TODO: Missed canonicalization - hoist 'not'?
+
 define i1 @not_select_cmpf(i1 %x, i32 %z, i32 %w, i1 %cond) {
 ; CHECK-LABEL: @not_select_cmpf(
 ; CHECK-NEXT:    [[CMPF:%.*]] = icmp ugt i32 [[Z:%.*]], [[W:%.*]]